Methane mitigation timelines to inform energy technology evaluation

Changing atmospheric concentrations of greenhouse gases are associated with changes in global mean temperature (with a time lag) and a range of impacts related to temperature or more directly to heat fluxes [41]. Climate change mitigation targets are commonly formulated around a recommended temperature threshold [3], from which an RF stabilization level can be derived. We use a 3 W m⁻² global RF stabilization target, which in equilibrium is roughly equivalent to a 2 °C temperature change [1] from pre-industrial levels, a commonly cited climate target [3]. A range of scenarios stabilizing at this level is determined [40, 42], with stabilization occurring within a range of approximately 15 years up to 2050 (see section S1). A stabilization year of 2050, consistent with a 3 W m⁻² RF target and the RCP2.6 scenario [43, 44], is used as an example but we also examine the effect of earlier stabilization years.

Beginning in the year 2015, the global RF target required for stabilization in 2050, computed by subtracting the estimated RF due to legacy emissions (pre-2015 emissions remaining in the atmosphere in 2050) from 3 W m⁻², is found to be 1.6 W m⁻² of which an estimated 70% or 1.12 W m⁻² is attributable to global energy-related emissions [1]. In our model, the RF stabilization target for a specific energy sector is its fraction of the global energy-related RF target in proportion to its energy consumption today relative to total global energy consumption. The US road transportation sector constitutes about 4% of today's global primary energy consumption [45]. We consider as an example 36% of the US road transportation sector for our technology portfolio choice and an RF stabilization target (TRF) for this subsector of 1% of the global stabilization target, or 0.016 W m⁻². The benefits of planning for CH₄ mitigation would apply to larger energy end-use sectors as well. (The effect on our results of deviating from this particular sectoral RF target is discussed in section 3.3.)

Technologies emit multiple greenhouse gases, the three most significant being CO₂, CH₄ and nitrous oxide (N₂O), indexed by $i=K,M,N,$ respectively. The RF following the use of a technology can be linearly approximated by a function of the emission intensities of these gases, and their radiative efficiencies and atmospheric lifetimes [1]. However, in sections 3.3 and S10 the effects of variable gas lifetimes and nonlinearities in this relationship, due to the effect of changing background greenhouse gas concentrations on marginal RF, are studied [46]. Let b_ij denote the mass of gas i emitted by technology j per unit energy consumption, A_i the radiative efficiency of gas i, and ${f}_{i}(t,t^{\prime} )$ the impulse response function representing the fraction of gas i retained in the atmosphere at time t following emission at time $t^{\prime} ,$

$$\begin{eqnarray}&&{f}_{i}(t,t^{\prime} )=\mathrm{exp}\left(-\displaystyle \frac{t-t^{\prime} }{{\tau }_{i}}\right),\mathrm{for}\ i=M,N,\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{f}_{K}(t,t^{\prime} )={a}_{0}+\displaystyle \sum _{k=1}^{3}{a}_{k}\cdot \mathrm{exp}\left(-\displaystyle \frac{t-t^{\prime} }{{\tau }_{k}}\right).\end{eqnarray} \tag{ 2 }$$

Empirical values of A_i and the parameters in ${f}_{i}(t,t^{\prime} )$ for CO₂, CH₄ and N₂O [1] are given in section S2.

The instantaneous RF from unit energy consumption using technology j is ${\displaystyle \sum }_{i}{b}_{{ij}}{A}_{i}$ and the RF impact at evaluation time t of a pulse emission from unit energy consumption using technology j at emission time $t^{\prime}$ is

$$\begin{eqnarray}&&{\mathrm{RF}}_{j}\left(t,t^{\prime} \right)=\displaystyle \sum _{i}{b}_{{ij}}{A}_{i}{f}_{i}\left(t,t^{\prime} \right).\end{eqnarray} \tag{ 3 }$$

For sustained emissions occurring over time, prior to the evaluation time t, ${\mathrm{RF}}_{j}(t,t^{\prime} )$ in (3) represents the marginal RF impact at t of unit energy consumption at emission time $t^{\prime} .$ This corresponds to the absolute ICI metric [40] for technology j (see section S5).

Using the same parameters, technology j's impact based on the GWP(τ), is

$$\begin{eqnarray}&&{\mathrm{GWP}}_{j}(\tau )=\displaystyle \sum _{i}{b}_{{ij}}{\mathrm{GWP}}_{i}(\tau ),\end{eqnarray} \tag{ 4 }$$

in grams CO₂-equivalent per unit energy consumption, where

$$\begin{eqnarray}&&{\mathrm{GWP}}_{i}(\tau )=\displaystyle \frac{{\displaystyle \int }_{t^{\prime} }^{t^{\prime} +\tau }{A}_{i}{f}_{i}(t^{\prime\prime} ,t^{\prime} ){\rm{d}}t^{\prime\prime} }{{\displaystyle \int }_{t^{\prime} }^{t^{\prime} +\tau }{A}_{K}{f}_{K}(t^{\prime\prime} ,t^{\prime} ){\rm{d}}t^{\prime\prime} }\end{eqnarray} \tag{ 5 }$$

and τ is the integration horizon.

Life cycle emissions intensities b_ij are obtained from the GREET model (https://greet.es.anl.gov) for three pairs of transportation technologies, where 'technology' refers to the combined fuel and vehicle jointly. Emissions intensities are current estimates for the US, and values may vary geographically and over time. Significant reductions in CH₄ emissions may be possible [47]. The sensitivity of our results to such variations is discussed in section 3.3.

For each technology pair the CH₄-heavy h and CH₄-light l are chosen so that ${b}_{{Mh}}\gt {b}_{{Ml}}$ (figures 1(a) and (b)). CH₄-heavy technologies compressed natural gas (CNG), algae biodiesel (algae), and renewable natural gas (RNG) exhibit higher instantaneous RF than their CH₄-light counterparts gasoline, electric vehicle (EV), and switchgrass ethanol (switchgrass) (figure 1(c)) but lower GWP(100)-based impacts (figure 1(d)), due to the higher radiative efficiency but faster decay time of CH₄ relative to CO₂. See table S3 for numerical values associated with figures 1(a)–(d).

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Since CH₄ decays much faster than CO₂ (and N₂O), the RF induced by an initial pulse emission from a CH₄-heavy technology falls faster with t and its GWP(τ) falls faster with τ than from its CH₄-light counterpart (figures 2(a) and (b)). The initial values in figure 2(a) correspond to the bars in figure 1(c), and the GWP(τ) values at τ = 100 in figure 2(b) correspond to the bars in figure 1(d). To the extent possible, technologies in each pair are matched in terms of their GWP(35) impact values, where 35 years is the stabilization horizon between 2015 and 2050.

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Energy technologies emit greenhouse gases as sustained streams over time rather than as a single pulse. We use a discrete time approximation of energy consumption where emissions occur as a pulse at the end of each year $t^{\prime} =0,\ldots ,{t}_{{\rm{S}}}.$

Let ${c}_{t^{\prime} }$ denote energy demand in year $t^{\prime}$ and ${x}_{{jt}^{\prime} }$ the fraction of ${c}_{t^{\prime} }$ supplied by technology j in year $t^{\prime} .$ A technology portfolio p is defined by the set ${x}_{{jt}^{\prime} }$ over time $t^{\prime} =0,\ldots ,{t}_{{\rm{S}}},$ and ${\mathrm{RF}}_{p}({t}_{{\rm{S}}})$ denotes the total RF induced by the portfolio at the end of the stabilization year t_S. In the model presented here, the technology planning horizon coincides with the RF stabilization year, given the concurrence of commonly suggested stabilization horizons [43, 48] and timelines for technology development and infrastructure planning [49]. However, the model could be adapted to cases where the planning and stabilization horizons differ (see section S6.1). The optimization model that selects a technology portfolio and energy consumption levels to maximize total consumption, while satisfying the RF target in the stabilization year, is given below.

Optimization model

$$\begin{eqnarray*}&&\underset{{c}_{t^{\prime} },{x}_{{jt}^{\prime} }\forall j,t^{\prime} }{\mathrm{Max}}\quad \displaystyle \sum _{t^{\prime} =0}^{{t}_{{\rm{S}}}}{c}_{t^{\prime} }\\ &&{\rm{s.t.}}\ \quad {c}_{t^{\prime} }={c}_{t^{\prime} -1}(1+{g}_{t^{\prime} })\ \mathrm{for}\ \ 1\leqslant t^{\prime} \leqslant {t}_{{\rm{S}}},\\ &&\qquad \quad {\mathrm{RF}}_{p}({t}_{{\rm{S}}})\leqslant \mathrm{TRF},\\ &&\qquad \quad {x}_{{jt}^{\prime} }\in [0,1]\ \mathrm{and}\ \displaystyle \sum _{j}{x}_{{jt}^{\prime} }=1,\\ &&\qquad \qquad \ \mathrm{for}\ j=h,l\ \mathrm{and}\ 0\leqslant t^{\prime} \leqslant {t}_{{\rm{S}}},\end{eqnarray*}$$

where the objective function represents total energy consumption, the first constraint defines the energy consumption profile based on growth rate ${g}_{t^{\prime} }$ in year $t^{\prime}$ and the second constraint ensures that RF does not exceed the target (TRF) in the stabilization year.

The portfolio contribution to RF, given by ${\mathrm{RF}}_{p}({t}_{{\rm{S}}}),$ is

$$\begin{eqnarray}&&{\mathrm{RF}}_{p}({t}_{{\rm{S}}})=\displaystyle \sum _{t^{\prime} =0}^{{t}_{{\rm{S}}}}{c}_{t^{\prime} }\displaystyle \sum _{j}{x}_{{jt}^{\prime} }{\mathrm{RF}}_{j}({t}_{{\rm{S}}},t^{\prime} ).\end{eqnarray} \tag{ 6 }$$

${\mathrm{RF}}_{p}({t}_{{\rm{S}}})$ is the sum of RF impacts in the stabilization year of all prior portfolio emissions. ${\mathrm{RF}}_{j}({t}_{{\rm{S}}},t^{\prime} )$ represents the marginal RF impact of unit energy consumption using technology j in emission year $t^{\prime} .$ Using (6) in the model simplifies its solution as we can first determine the optimal technology choice in each year by minimizing ${\mathrm{RF}}_{p}({t}_{{\rm{S}}})$ and then maximize energy consumption using the optimal portfolio.

Since the model constrains RF only in the stabilization year, TRF overshoots are possible. An additional set of constraints

$$\begin{eqnarray}&&{\mathrm{RF}}_{p}(t)\leqslant \mathrm{TRF}\ \mathrm{for}\ 0\lt t\lt {t}_{{\rm{S}}},\end{eqnarray} \tag{ 7 }$$

(referred to as overshoot constraints) are also presented to assess the impact of overshoot restrictions on optimal energy consumption levels. Overshoots could be restricted through policies that separately cap short- and long-lived greenhouse gases [5].

The model is applied to the three transportation technology pairs shown in figure 1. We consider annual energy consumption growth rates of $0\%,$ representing flat consumption. (In section S6.2, we also consider how the results change under an energy consumption growth rate of $1.2\%$ [45].) Additionally, we consider the effect of uncertainty in the stabilization horizon (see section S9), based on a 15 year range of stabilization years given a plausible set of emissions scenarios for stabilizing RF at 3 W m⁻² (see section 3.3 and section S1).

We compare the optimal technology portfolio based on the dynamic emissions impact evaluation, with the portfolio (and energy consumption) that would be obtained using the GWP. This allows us to estimate the gains of this approach over the standard GWP-based method for technology evaluation. CO₂-equivalent emissions are determined using the GWP and treated as CO₂ when evaluating the RF impact in the stabilization year. (This is similar to the approach outlined above but uses the GWP in place of a marginal RF impact based metric.) Therefore, the GWP-based estimate of RF impact in the stabilization year of technology j per unit energy consumption in year $t^{\prime}$ is ${\mathrm{GWP}}_{j}(\tau ){A}_{K}{f}_{K}({t}_{{\rm{S}}},t^{\prime} ),$ where ${\mathrm{GWP}}_{j}(\tau )$ is given by (4) (in units CO₂-equivalent per unit energy consumption), A_K is the radiative efficiency of CO₂, and ${f}_{K}({t}_{{\rm{S}}},t^{\prime} )$ is the fraction of CO₂ emitted at time $t^{\prime}$ remaining in the atmosphere at time t_S. Using this definition, the intended RF in year t_S, based on the GWP, of using technology portfolio p for the energy consumption stream ${c}_{0},\ldots ,{c}_{{t}_{{\rm{S}}}},$ is

$$\begin{eqnarray}&&{\mathrm{RF}}_{p}^{g}({t}_{{\rm{S}}})=\displaystyle \sum _{t^{\prime} =0}^{{t}_{{\rm{S}}}}{c}_{t^{\prime} }\displaystyle \sum _{j}{x}_{{jt}^{\prime} }{\mathrm{GWP}}_{j}(\tau ){A}_{K}{f}_{K}({t}_{{\rm{S}}},t^{\prime} ).\end{eqnarray} \tag{ 8 }$$

Equation (8) is used in the optimization model in place of ${\mathrm{RF}}_{p}({t}_{{\rm{S}}})$ given in (6) to determine the maximum energy consumption allowed by the GWP-based portfolio. We consider both GWP(100) and GWP(35) in our numerical simulations: GWP(100) because it is the most widely used metric and GWP(35) because it is consistent with our planning horizon of 35 years.

The optimal technology portfolio is determined by year-wise minimization of ${\mathrm{RF}}_{j}({t}_{{\rm{S}}},t^{\prime} )$ across technologies, which can yield a technology portfolio switching from the CH₄-heavy to the CH₄-light technology in an optimal switching year ${t}^{*}$. The maximum possible energy consumption is determined using the optimal technology portfolio. The results support the use of suitable CH₄-heavy technologies as bridging technologies, if the stabilization horizon is sufficiently long, i.e. ${t}^{*}$ exists and has not already passed. All three technology pairs shown in figure 1 satisfy these conditions. The marginal RF impact resulting from using each technology over time, in an example stabilization year of 2050, is shown in figure 3. The general solution to the optimal portfolio problem is given in sections S6.1 and S6.2.

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The optimal switching-to-stabilization time span is 22 years for CNG and gasoline, 14 years for algae and EV, and 19 years for RNG and switchgrass. Using a stabilization horizon of 35 years (2015–2050), it is optimal to use CNG for 13 years, algae for 21 years, and RNG for 16 years, followed by a switch to gasoline, EV, and switchgrass, respectively. If the stabilization year is shifted up to 2043 (the middle of the modeled range of years discussed in section 2.1), the optimal switching year for each technology pair shifts by 7 years, keeping the same time span between switching and stabilization (see section S9).

We calculate the maximum allowed gasoline-equivalent energy consumption for individual technologies in each technology pair and compare the values to the consumption using the optimal switching portfolio (figure 4). The optimal switching portfolio increases the allowed energy consumption relative to each individual technology alone. The percentage energy consumption gains relative to the individual CH₄-light and CH₄-heavy technologies are shown in figures 4(b) and (c), respectively.

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The results call into question the benefits of CNG at current CH₄ leakage estimates, given the relatively small gain of 2% using a switching portfolio (from CNG to gasoline) over using gasoline alone, and the dominance of gasoline-based vehicles and infrastructure today. The investment required to make the transition to CNG may not be justified by the modest gains in energy consumption. Furthermore, the results demonstrate the higher energy consumption supported by the lower emissions technologies (EV, algae and switchgrass, RNG). The CNG, gasoline pair does not meet projected energy demand under this RF target.

The RF trajectories for individual technologies in each pair, and their optimal switching portfolios, are shown in figures 5(a)–(c). While the RF constraint is met in the stabilization year, the RNG-switchgrass optimal switching portfolio exhibits limited overshoots prior to the stabilization year, peaking at approximately 11% above the sector RF target (0.1% of the global target) in the switching year. Early overshoots can be concerning if they are relatively large and long-lasting, and if policy targets are set to be consistent with climate system thresholds above which abrupt climate changes may occur [50, 51].

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An early RF overshoot can occur with a switching portfolio if the CH₄-heavy technology has a sufficiently high CH₄ intensity relative to the CH₄-light technology (if the percent difference is significantly large). Early consumption using a CH₄-heavy technology can in this case lead to an increase in RF followed by a rapid decrease after switching, resulting in a switching year 'peak' RF that exceeds the RF constraint. This effect is observed for the RNG-switchgrass portfolio, whereas the CNG-gasoline and algae-EV portfolios do not result in an RF overshoot (figure 5). See section S6.4.

Overshoots can be avoided by choosing an earlier stabilization year (if averse to the risk of a temporary overshoot) (figure S7). Overshoots could also be restricted in a policy context where gases are capped separately. A 'multi-basket' policy could be formulated to achieve an overshoot restriction. In this case planning to transition from a CH₄-heavy to a CH₄-light technology still provides an advantage over applying the GWP, as the switching portfolio will allow greater energy consumption while meeting the RF constraint (see figure 4(a) and section S8).

The GWP-based optimal technology portfolio is determined by using the intended RF based on GWP $(\tau )$ from (8) instead of (6) in the technology portfolio optimization model (see section S7 for the general solution and proof). Using the GWP(100), the CH₄-heavy technologies in each pair are used to satisfy the entire portfolio, since they have lower GWP(100)-evaluated impacts than their CH₄-light counterparts (figure 2(b) at $\tau =100$). The GWP(100)-based intended RF underestimates actual RF in the stabilization year, thus allowing higher energy consumption and overshooting the RF target (black lines in figure 5). If instead the RF constraint is forced to be met, the allowed energy consumption can be much lower when applying the GWP for technology evaluation than when planning for a switching portfolio (20% lower using the GWP(100) with a cap versus the RNG-switchgrass portfolio, figure 4 and section S8).

Since the CH₄-light technology has a lower GWP(35) than its CH₄-heavy counterpart for each technology pair (figure 2(b) at $\tau =35$), the CH₄-light technology is selected over the entire horizon when the GWP(35) is applied. Because the integration horizon is the same as the stabilization horizon, the GWP(35)-based intended RF is consistent with the actual RF. Therefore, the maximum energy consumption allowed by the GWP(35) (using equation (8)) is the same as that allowed by the CH₄-light technologies (equation (6)) while meeting the RF target (figure 4, dashed grey lines in figure 5). The switching portfolio can support greater energy consumption than the GWP(35)-based selection of the CH₄-light technology alone. The RNG-switchgrass portfolio allows a 15% energy gain over switchgrass alone. The algae-EV portfolio allows a 12% gain over EV alone, and CNG-gasoline allows for a 2% gain over gasoline alone. See figure 4(b) and section S7.

The energy gains of the switching portfolio over using the CH₄-light technology alone are determined by the percent difference in CH₄ intensities of the CH₄-heavy and CH₄-light technologies. The percent energy gains of the dynamic evaluation method can be larger if this difference is greater (as long as the difference is not so large that the CH₄-heavy technology is no longer selected over the CH₄-light technology). See figure 4 and section S7.

Here we discuss the robustness of the results presented to uncertainties in the stabilization year, the radiative efficiencies and lifetimes of greenhouse gases, and the sectoral RF target. We find that the benefits of technology transition portfolios are relatively robust to these uncertainties, suggesting the utility of this approach to technology evaluation (given a 3 W m⁻² global RF stabilization target) despite an inherent lack of knowledge about the future. We also discuss how the insights from this research apply given changing emissions intensities of technologies, variable technology costs and quality of service, and alternative global RF stabilization targets.

Sensitivity to stabilization year uncertainty. We compare the optimal decisions based on a plausible range of stabilization horizons for a 3 W m⁻² RF target (section S1). Examining the stochastic case, where technologies are evaluated based on the expected stabilization year (2043) but actual stabilization may occur earlier or later in the range 2035–2050, the switching portfolio still outperforms other portfolios (CH₄-light/GWP(35), CH₄-heavy, capped GWP(100)), with the energy consumption gains of the switching portfolio only modestly reduced. Stabilization year uncertainty can reduce the energy consumption gains (in gasoline-equivalent km) of the switching portfolios by 4%–6%. See table S9. Therefore, for these technology pairs, the performance of an optimal portfolio is relatively insensitive to uncertainty in the stabilization year.

Sensitivity to a changing background concentration of greenhouse gases. We test the robustness of the gains of the dynamic emissions evaluation model over the static GWP, given that the radiative efficiencies of CO₂, CH₄, and N₂O and the lifetime of CH₄ are likely to vary over time as the background concentrations of greenhouse gases change. To test the sensitivity of our results to these changes we select the RCP2.6 [44] as a sample scenario. (The RCP2.6 is just one possible 3 W m⁻²-compliant scenario but is reasonable for demonstrating the rough scale of the effect of changing radiative efficiencies and CH₄ lifetimes.)

We find that the results are robust to changing radiative efficiencies and a changing CH₄ lifetime. If technology switching decisions are made using the assumptions of constant radiative efficiency and CH₄ lifetime (representing the forward-looking part of the model), but energy consumption and RF scenarios are determined based on a changing radiative efficiency and a variable lifetime (representing the realized outcome), the gains of the switching portfolios are preserved. Specifically, the gains over the CH₄-heavy (CH₄-light) technology are 17% (4%) for CNG-gasoline, 15% (16%) for algae-EV and 56% (25%) for RNG-switchgrass. This is compared to gains of 17% (2%), 12% (12%), and 51% (15%), respectively, under the constant radiative efficiency case. See section S10, figures S11 and S12. We further examine the impact of other scenarios where greenhouse gas emissions and concentrations continue to increase over time (namely, RCP6 and RCP8.5) and find that the gains of the switching portfolio over the CH₄-light and CH₄-heavy technologies are comparable to the results shown for RCP2.6. See section S10.

Sensitivity to sectoral RF target. Variations in the fraction of the global RF target allocated to a given sector would change the energy consumption levels in our numerical analysis, but would not affect the technology transition (or CH₄ mitigation) timeline in the optimal portfolio. (The change in energy consumption due to a change in the RF target can be inferred from equation (S11) in proposition S2. The optimal switching timeline is unaffected as equation (S6) is independent of the RF target. See sections S6.2 and S6.1, respectively.)

Effect of variable emissions intensities. CH₄ intensities depend on venting and leakage in the production or supply infrastructure and are expected to vary across geographical locations and over time. Significant reductions may be possible [47]. If the CH₄ emissions intensity of the CH₄-heavy technologies decreases, as compared to the current US estimates on which the results are based , switching will move closer to the intended stabilization year up to a point where switching is no longer optimal. We can estimate how significant these CH₄-emissions intensity reductions would need to be to make switching suboptimal. Holding other emissions intensities constant, if the CH₄ emissions intensity of CNG decreases by 73% or greater, switching to gasoline is no longer optimal. Reductions of the algae (RNG) CH₄ emissions intensity of 46% (66%) would make switching to EV (switchgrass) suboptimal. See section S6.5.

Effect of technology costs or quality of service. The model is constructed to determine whether a dynamic emissions impact evaluation can yield significant gains, not to represent an expected outcome scenario in the real marketplace. The numerical results we present would only hold in the marketplace (with the lowest emissions technology pair representing the optimal portfolio) if technology costs and service level were comparable, energy consumption were equated to economic benefit, and the technologies examined represented the full range of options available. Although these conditions are not met, the model demonstrates the potential for substantial energy consumption gains (and associated economic benefits) from a dynamic emissions impact evaluation for planning technology switching or CH₄ mitigation, under a single- or multi-basket emissions cap. The dynamic emissions impacts we quantify are one important input into technology decisions in the marketplace under a climate policy, but the transition timelines and choice between technology pairs would also depend on the relative costs and service limitations of technologies (e.g. EV range constraints), as well as the benefits of the energy services provided.

Effect of alternative global RF stabilization targets. For stabilization horizons stretching, for example, to 2100 either due to changes in assumptions regarding the range of plausible emissions reduction rates or higher RF stabilization levels, the results presented here would change, with CH₄-heavy technologies favored for a longer period of time. In this case, the instantaneous measure of RF impact in the stabilization year could result in substantial RF overshoots in earlier years, making the emissions and technology evaluation approach described here less attractive. We note that century scale horizons are longer than practical for technology planning, and are therefore outside the scope of this paper. Furthermore, planning for an earlier-than-realized stabilization year would reduce the risk of RF overshoots.